VARSY PM5

1. VARSY PM5 Robin Hogan, Nicola Pounder, Brian Tse, Chris Westbrook University of Reading 5 June 2013

2. Overview • Retrieval of a “riming factor” • Scattering by snowflakes • Kalman smoother capability • Retrieval of aerosol properties • Parallelization

3. Unified retrieval Ingredients developed Done since April Not yet developed 1. Define state variables to be retrieved Use classification to specify variables describing each species at each gate Ice and snow: extinction coefficient, N0’, lidar ratio, riming factor Liquid: extinction coefficient and number concentration Rain: rain rate, drop diameter and melting ice Aerosol:extinction coefficient, particle size and lidar ratio 2. Forward model 2a. Radar model With surface returnand multiple scattering 2b. Lidar model Including HSRL channels and multiple scattering 2c. Radiance model Solar & IR channels 4. Iteration method Derive a new state vector: Gauss-Newton or quasi-Newton scheme Not converged 3. Compare to observations Check for convergence Converged 5. Calculate retrieval error Error covariances & averaging kernel Proceed to next ray of data

4. CloudSat EarthCARE Z EarthCARE Doppler • Worst case error in Tropics (lowest PRF) due to satellite motion, finite sampling, SNR conditions • But no riming, non-uniform beam-filling or vertical air motion! PavlosKollias Note higher radar sensitivity

5. Prior information about size distribution • Radar+lidar enables us to retrieve two variables: extinction a and N0* (a generalized intercept parameter of the size distribution) • When lidar completely attenuated, N0* blends back to temperature-dependent a-priori and behaviour then similar to radar-only retrieval • Aircraft obs show decrease of N0* towards warmer temperatures T • (Acually retrieve N0*/a0.6 because varies with T independent of IWC) • Trend could be because of aggregation, or reduced ice nuclei at warmer temperatures • But what happens in snow where aggregation could be much more rapid? Delanoe and Hogan (2008)

6. Extending ice retrievals to riming snow • Retrieve a riming factor (0-1) which scales b in mass=aDb between 1.9 (Brown & Francis) and 3 (solid ice) 0.9 0.8 0.7 0.6 • Heymsfield & Westbrook (2010) fall speed vs. mass, size & area • Brown & Francis (1995) ice never falls faster than 1 m/s Brown & Francis (1995)

7. Examples of snow35 GHz radar at Chilbolton 1 m/s: no riming or very weak 2-3 m/s: riming? • PDF of 15-min-averaged Doppler in snow and ice (usually above a melting layer)

8. Simulated observations – no riming

9. Simulated retrievals – no riming

10. Simulated retrievals – riming

11. Simulated observations – riming

12. Ongoing riming work • EarthCARE Doppler radar offers interesting possibilities for retrieving rimed particles in cases without significant vertical motion • Need to first have cleaned up non-uniform beam-filling effects • Note we neglected spatial correlations of random error on 100-m scale • Retrieval development at the stage of testing ideas; validation required! • Some future work • Simone Tanelli has offered a dataset of observed airborne radar data as observed, with EarthCARE NUBF, and with NUBF correction • Remaining unknowns (common to many algorithms) • In ice cloud we have good temperature-dependent prior for number concentration parameter “N0*”: what should this be for snow? • How can we get a handle on the supercooled liquid content in deep ice & snow clouds, even just a reasonable a-priori assumption? • Backscatter of snow is uncertain…

13. Radar backscatter of snow • So far we are assuming homogeneous ice-air spheroids for both ice-cloud particles and snowflakes (Hogan et al. 2012) • This is fine for size < wavelength, but for larger snowflakes the backscatter is increasingly underestimated • Rayleigh-Gans approximation is applicable: describe particle by A(z) • Have derived a formula for backscatter of ensemble of snow particles 1 mm ice 1 cm snow

14. New formula for backscatter • Rayleigh-Gans formula: • Fourier-like decomposition of A(z): • Assume amplitudes decrease at smaller scales as a power-law • Formula for backscatter: • Wavenumber k • Volume V • Radius zmax • Power-law parameters b & g

15. Kalman smoother • Aerosol information is noisy: we need intelligent smoothing • Ordinary retrieval: cost function has observation and a priori terms • Kalman smoother forward pass: add term penalizing differences from the retrieval at the previous ray n-1, where S is the error covariance matrix for that retrieval and D is an additional error to account for the spatial decorrelation: • Kalman smoother reverse pass: penalize differences from both ray ahead and ray behind (doubles algorithm run time!): • So far, the Kalman smoother (first-pass only so far) can be used on any state variable with arbitrary D (but must be a diagonal matrix); tested on ice extinction and aerosol number concentration • Reverse pass involves reading back in saved rays: should be easy

16. Before… • CloudSat forward model • CloudSat observations • Calipso forward model • Calipso observations • Retrieved extinction coefficient • Retrieved number concentration

17. …after • CloudSat forward model • CloudSat observations • Calipso forward model • Calipso observations • Retrieved extinction coefficient • Retrieved number concentration

18. Aerosol retrieval • All retrieved species are described by two main variables: a measure of number concentration and one other variable; from these, all moments of the size distribution to be computed • We use median volume diameter D0 and total number concentration • With Calipso (one observable), have to: • Prescribe D0 (currently 0.5 microns) • Prescribe aerosol medium (currently ammonium sulphate); or could be from lon-lat climatology or previous retrieval/classification in the chain • Assume spherical particles; in principle could be changed • With EarthCARE: • Two solar wavelengths: retrieve size • HSRL bscat-ext ratio: size ambiguous; use with depol to retrieve type first? • Signal very noisy so Kalman smoother essential…

19. Calipso forward model • Calipsoobs • Optical depth • Aerosol number conc • Aerosol mass content Retrieve each pixel independently

20. Calipso forward model • Calipsoobs • Optical depth • Aerosol number conc • Aerosol mass content Splines to smooth vertically

21. Calipso forward model • Calipsoobs • Optical depth • Aerosol number conc • Aerosol mass content Vertical smoothing plus Kalman smoother

22. Optimization and parallelization • Levenberg-Marquardt needs fewer iterations to converge, but requires Jacobian matrix to be computed: slow • In principle, calculation of an m x nJacobian matrix can be parallelized with m or n threads in parallel (which ever is smaller) • Provisional results: • Multi-core CPU: Most current PCs have multiple cores (2-8) and with OpenMP the Jacobian calculation has been successfully sped up by almost a factor of the number of cores (factor 3.6 for 4 cores) • GPU: We been experimenting with a Quadro 4000 Nvidia card that in principle can run ~1500 threads in parallel, although each thread much slower than a CPU. In our case n ~ m ~ 100 and for 100 threads the GPU is slower. We are working on improving the ability to combine parallelization of the physics with parallelization of the Jacobian.

23. Remaining algorithm development • Parallelization • Explore parallelization of physics compatible with automatic differentiation • Establish best approach: multi-core CPU versus GPU • Forward models • Finish implementation of LIDORT solar radiance model • Ice clouds • Test Doppler impact using data from Simone or Pavlos • Add new snow scattering model (needs further work) • Add Baran phase functions for MSI wavelengths • Liquid clouds • Test impact of solar radiances on retrievals • Test size retrieval from two solar wavelengths • Can radiances + radar PIA provide integral constraints that EarthCARE won’t get from lidar multiple scattering? • Aerosols • Test impact of solar radiances on retrievals, e.g. particle size

25. How complex must scattering models be? • “Soft sphere” described by appropriate mass-size relationship • Good agreement between aircraft & 10-cm radar using Brown & Francis mass-size relationship (Hogan et al. 2006) • Poorer for millimeter wavelengths (Petty & Huang 2010) • In ice clouds, 94 GHz underestimated by around 4 dB (Matrosov and Heymsfield 2008, Hogan et al. 2012) -> poor IWC retrievals • Horizontally oriented “soft spheroid” of aspect ratio 0.6 • Aspect ratio supported for ice clouds by aggregation models (Westbrook et al. 2004) & aircraft (Korolev & Isaac 2003) • Supported by dual-wavelength radar (Matrosov et al. 2005) and differential reflectivity (Hogan et al. 2012) for size <= wavelength • Tyynela et al. (2011) calculations suggested this model significantly underestimated backscatter for sizes larger than the wavelength • Leinonen et al. (2012) came to the same conclusions in half of their 3- wavelength radar data (soft spheroids were OK in the other half) • Realistic snow particles and DDA (or similar) scattering code • Assumptions on morphology need verification using real measurements

26. Spheres versus spheroids Transmitted wave Spheroid Sphere Sphere: returns from opposite sides of particle out of phase: cancellation Spheroid: returns from opposite sides not out of phase: higherb Hogan et al. (2011)